Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1782 conjugacy classes of subgroups.
The subgroup lattice has 620 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D3×Q82 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | Q8×#237 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×Q8×SD16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | Q8×#216 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | Q8×#214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #81906 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #81893 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #81061 | C2 | 1 | 3 | yes | maximal |
| 9 | #81056 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #81043 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #81011 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | Q8×Dic12 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | Q8×ΓL(1,𝔽25) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C4×#915 | C2 | 1 | 3 | yes | maximal |
| 15 | #79634 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | Q8×#137 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C3×Q82 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×D4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×#67 | — | 2 | 1 | no | — |
| 20 | C2×Q8×Dic3 | — | 2 | 1 | no | — |
| 21 | C2×#915 | C22 | 1 | 1 | yes | characteristic |
| 22 | #5728 | C22 | 1 | 3 | yes | — |
| 23 | D3×C4⋊Q8 | — | 2 | 3 | no | — |
| 24 | D3×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 25 | #5722 | — | 2 | 3 | no | — |
| 26 | #5722 | C22 | 1 | 3 | yes | — |
| 27 | #5721 | C22 | 1 | 3 | yes | — |
| 28 | #5635 | — | 2 | 3 | no | — |
| 29 | #5622 | — | 2 | 3 | no | — |
| 30 | C4×D3×Q8 | — | 2 | 1 | no | — |
| 31 | C4×D3×Q8 | C22 | 1 | 3 | yes | — |
| 32 | C4×D3×Q8 | C22 | 1 | 1 | yes | characteristic |
| 33 | Q8×Dic6 | — | 2 | 1 | no | — |
| 34 | Q8×Dic6 | C22 | 1 | 3 | yes | — |
| 35 | Q8×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 36 | Q8×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 37 | #5543 | C22 | 1 | 3 | yes | — |
| 38 | C4×#237 | C22 | 1 | 3 | yes | — |
| 39 | C3×#498 | C22 | 1 | 3 | yes | — |
| 40 | C3×#476 | C22 | 1 | 3 | yes | — |
| 41 | C3×#475 | C22 | 1 | 3 | yes | — |
| 42 | C3×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 43 | C3×C4×SD16 | C22 | 1 | 3 | yes | — |
| 44 | #5164 | C22 | 1 | 3 | yes | — |
| 45 | #5094 | C22 | 1 | 3 | yes | — |
| 46 | #5091 | C22 | 1 | 3 | yes | — |
| 47 | #5080 | C22 | 1 | 3 | yes | — |
| 48 | #5078 | C22 | 1 | 3 | yes | — |
| 49 | C4×#216 | C22 | 1 | 3 | yes | — |
| 50 | Q8×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 51 | #5021 | C22 | 1 | 3 | yes | — |
| 52 | C4×#214 | C22 | 1 | 3 | yes | — |
| 53 | #5008 | C22 | 1 | 3 | yes | — |
| 54 | #4861 | C22 | 1 | 3 | yes | — |
| 55 | #4861 | C22 | 1 | 6 | yes | — |
| 56 | #4857 | C22 | 1 | 6 | yes | — |
| 57 | #4856 | C22 | 1 | 6 | yes | — |
| 58 | #4856 | C22 | 1 | 6 | yes | — |
| 59 | #4854 | C22 | 1 | 6 | yes | — |
| 60 | #4853 | C22 | 1 | 3 | yes | — |
| 61 | #4850 | C22 | 1 | 3 | yes | — |
| 62 | #4850 | C22 | 1 | 3 | yes | — |
| 63 | #4837 | C22 | 1 | 3 | yes | — |
| 64 | #4831 | C22 | 1 | 3 | yes | — |
| 65 | #4802 | C22 | 1 | 3 | yes | — |
| 66 | #4796 | C22 | 1 | 6 | yes | — |
| 67 | #4789 | C22 | 1 | 3 | yes | — |
| 68 | #4771 | C22 | 1 | 3 | yes | — |
| 69 | #4759 | C22 | 1 | 6 | yes | — |
| 70 | #4757 | C22 | 1 | 3 | yes | — |
| 71 | C4×Dic12 | C22 | 1 | 3 | yes | — |
| 72 | C4×ΓL(1,𝔽25) | C22 | 1 | 3 | yes | — |
| 73 | #4682 | C22 | 1 | 3 | yes | — |
| 74 | #4679 | C22 | 1 | 3 | yes | — |
| 75 | Q8×#41 | — | 3 | 1 | no | — |
| 76 | C2×Q82 | — | 3 | 1 | no | — |
| 77 | #3387 | — | 3 | 3 | no | — |
| 78 | #3387 | — | 3 | 3 | no | — |
| 79 | #3385 | — | 3 | 3 | no | — |
| 80 | #3385 | — | 3 | 3 | no | — |
| 81 | Q8×Q16 | — | 3 | 1 | no | — |
| 82 | Q8×Q16 | — | 3 | 1 | no | — |
| 83 | Q8×SD16 | — | 3 | 1 | no | — |
| 84 | Q8×SD16 | D3 | 1 | 1 | yes | characteristic, complemented |
| 85 | #3165 | — | 3 | 3 | no | — |
| 86 | #3079 | — | 3 | 3 | no | — |
| 87 | #3078 | — | 3 | 3 | no | — |
| 88 | Q8×M16 | — | 3 | 1 | no | — |
| 89 | C4×#137 | — | 3 | 3 | no | — |
| 90 | C22×C3×Q8 | — | 2 | 1 | no | — |
| 91 | C2×D3×Q8 | — | 2 | 3 | no | — |
| 92 | C2×D3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 93 | C2×D3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×#237 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C3×SD16 | C23 | 1 | 1 | yes | characteristic |
| 96 | C3×C4⋊Q8 | — | 2 | 3 | no | — |
| 97 | C3×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 98 | C3×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 99 | C3×C22⋊Q8 | — | 2 | 3 | no | — |
| 100 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 101 | C3×C4×Q8 | C23 | 1 | 3 | yes | — |
| 102 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 103 | C3×C4×D4 | C23 | 1 | 3 | yes | — |
| 104 | #946 | — | 2 | 3 | no | — |
| 105 | Q8×Dic3 | — | 2 | 1 | no | — |
| 106 | Q8×Dic3 | — | 2 | 1 | no | — |
| 107 | Q8×Dic3 | — | 2 | 3 | no | — |
| 108 | Q8×Dic3 | — | 2 | 3 | no | — |
| 109 | Q8×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 110 | Q8×Dic3 | C23 | 1 | 3 | yes | — |
| 111 | #944 | — | 2 | 3 | no | — |
| 112 | #944 | — | 2 | 6 | no | — |
| 113 | #944 | — | 2 | 3 | no | — |
| 114 | C2×#216 | C23 | 1 | 1 | yes | characteristic |
| 115 | D4×Dic3 | C23 | 1 | 3 | yes | — |
| 116 | C2×#214 | C23 | 1 | 1 | yes | characteristic |
| 117 | C4×#67 | — | 2 | 3 | no | — |
| 118 | C2×C4⋊Dic3 | — | 2 | 3 | no | — |
| 119 | #924 | — | 2 | 3 | no | — |
| 120 | C2×C4×Dic3 | — | 2 | 3 | no | — |
| 121 | #915 | Q8 | 1 | 8 | yes | direct product factor |
| 122 | C2×Dic12 | C23 | 1 | 1 | yes | characteristic |
| 123 | C2×ΓL(1,𝔽25) | C23 | 1 | 3 | yes | — |
| 124 | C2×ΓL(1,𝔽25) | C23 | 1 | 1 | yes | characteristic |
| 125 | #897 | — | 2 | 3 | no | — |
| 126 | #892 | C23 | 1 | 3 | yes | — |
| 127 | D3×C4⋊C4 | — | 2 | 3 | no | — |
| 128 | D3×C4⋊C4 | — | 2 | 3 | no | — |
| 129 | D3×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 130 | D3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 131 | #890 | C23 | 1 | 6 | yes | — |
| 132 | #889 | — | 2 | 6 | no | — |
| 133 | #888 | — | 2 | 3 | no | — |
| 134 | #888 | — | 2 | 3 | no | — |
| 135 | #888 | — | 2 | 3 | no | — |
| 136 | #888 | — | 2 | 6 | no | — |
| 137 | #888 | — | 2 | 3 | no | — |
| 138 | #888 | C23 | 1 | 6 | yes | — |
| 139 | #887 | — | 2 | 3 | no | — |
| 140 | #887 | — | 2 | 3 | no | — |
| 141 | #887 | — | 2 | 3 | no | — |
| 142 | #887 | D4 | 1 | 3 | yes | — |
| 143 | #887 | C23 | 1 | 3 | yes | — |
| 144 | #887 | C23 | 1 | 3 | yes | — |
| 145 | #67⋊C4 | — | 2 | 3 | no | — |
| 146 | #878 | — | 2 | 6 | no | — |
| 147 | #877 | — | 2 | 3 | no | — |
| 148 | C42×D3 | — | 2 | 3 | no | — |
| 149 | C42×D3 | C23 | 1 | 3 | yes | — |
| 150 | #869 | — | 2 | 3 | no | — |
| 151 | #869 | C23 | 1 | 3 | yes | — |
| 152 | #869 | C23 | 1 | 3 | yes | — |
| 153 | C4×Dic6 | — | 2 | 3 | no | — |
| 154 | C4×Dic6 | — | 2 | 3 | no | — |
| 155 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 156 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 157 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 158 | C3×#106 | C23 | 1 | 3 | yes | — |
| 159 | C3×#106 | C23 | 1 | 6 | yes | — |
| 160 | C3×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 161 | C3×#103 | C23 | 1 | 3 | yes | — |
| 162 | C3×#102 | C23 | 1 | 3 | yes | — |
| 163 | C3×C4×C8 | C23 | 1 | 3 | yes | — |
| 164 | #835 | C23 | 1 | 3 | yes | — |
| 165 | #832 | C23 | 1 | 3 | yes | — |
| 166 | #818 | C23 | 1 | 3 | yes | — |
| 167 | #818 | C23 | 1 | 6 | yes | — |
| 168 | #816 | C23 | 1 | 3 | yes | — |
| 169 | #816 | C23 | 1 | 3 | yes | — |
| 170 | #815 | C23 | 1 | 3 | yes | — |
| 171 | #815 | C23 | 1 | 3 | yes | — |
| 172 | Dic3⋊C8 | C23 | 1 | 6 | yes | — |
| 173 | #810 | C23 | 1 | 3 | yes | — |
| 174 | #810 | C23 | 1 | 3 | yes | — |
| 175 | #808 | C23 | 1 | 6 | yes | — |
| 176 | #808 | C23 | 1 | 3 | yes | — |
| 177 | #807 | C23 | 1 | 3 | yes | — |
| 178 | #807 | C23 | 1 | 6 | yes | — |
| 179 | C4⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 180 | C4×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 181 | C2×#137 | — | 3 | 1 | no | — |
| 182 | Q82 | — | 3 | 3 | no | — |
| 183 | Q82 | — | 3 | 3 | no | — |
| 184 | Q82 | — | 3 | 1 | no | — |
| 185 | Q82 | — | 3 | 1 | no | — |
| 186 | Q82 | — | 6 | 1 | no | — |
| 187 | Q82 | — | 6 | 3 | no | — |
| 188 | Q82 | C2×D3 | 1 | 1 | yes | characteristic |
| 189 | #557 | — | 3 | 3 | no | — |
| 190 | #554 | — | 3 | 3 | no | — |
| 191 | #554 | — | 6 | 3 | no | — |
| 192 | D4×Q8 | — | 6 | 1 | no | — |
| 193 | D4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 194 | #533 | — | 3 | 3 | no | — |
| 195 | #533 | — | 6 | 3 | no | — |
| 196 | C2×C4⋊Q8 | — | 3 | 3 | no | — |
| 197 | C2×C4⋊Q8 | — | 6 | 3 | no | — |
| 198 | C4×#41 | — | 3 | 3 | no | — |
| 199 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 200 | C2×C4×Q8 | — | 3 | 3 | no | — |
| 201 | C2×C4×Q8 | — | 6 | 1 | no | — |
| 202 | C2×C4×Q8 | — | 6 | 1 | no | — |
| 203 | #501 | — | 3 | 6 | no | — |
| 204 | #501 | — | 3 | 6 | no | — |
| 205 | #500 | — | 3 | 3 | no | — |
| 206 | #500 | — | 3 | 3 | no | — |
| 207 | #498 | — | 3 | 3 | no | — |
| 208 | #498 | C2×D3 | 1 | 3 | yes | — |
| 209 | #479 | — | 3 | 6 | no | — |
| 210 | #479 | — | 3 | 6 | no | — |
| 211 | #477 | — | 3 | 3 | no | — |
| 212 | #477 | — | 3 | 3 | no | — |
| 213 | #477 | — | 3 | 3 | no | — |
| 214 | #477 | — | 3 | 3 | no | — |
| 215 | #476 | — | 3 | 3 | no | — |
| 216 | #476 | C2×D3 | 1 | 3 | yes | — |
| 217 | #475 | — | 3 | 3 | no | — |
| 218 | #475 | — | 3 | 6 | no | — |
| 219 | #475 | C2×D3 | 1 | 3 | yes | — |
| 220 | #474 | — | 3 | 6 | no | — |
| 221 | #446 | — | 3 | 3 | no | — |
| 222 | #446 | — | 3 | 3 | no | — |
| 223 | C8×Q8 | — | 3 | 1 | no | — |
| 224 | C8×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 225 | #441 | — | 3 | 3 | no | — |
| 226 | #441 | — | 3 | 3 | no | — |
| 227 | #440 | — | 3 | 3 | no | — |
| 228 | #440 | — | 3 | 3 | no | — |
| 229 | C4×Q16 | — | 3 | 3 | no | — |
| 230 | C4×Q16 | — | 3 | 3 | no | — |
| 231 | C4×SD16 | — | 3 | 3 | no | — |
| 232 | C4×SD16 | C2×D3 | 1 | 3 | yes | — |
| 233 | #428 | — | 3 | 6 | no | — |
| 234 | #428 | — | 3 | 3 | no | — |
| 235 | #423 | — | 3 | 3 | no | — |
| 236 | #419 | — | 3 | 3 | no | — |
| 237 | #417 | — | 3 | 3 | no | — |
| 238 | C4×M16 | — | 3 | 3 | no | — |
| 239 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 240 | C2×C3×Q8 | — | 2 | 3 | no | — |
| 241 | C2×C3×Q8 | — | 4 | 4 | no | — |
| 242 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 244 | C2×C3×D4 | C24 | 1 | 1 | yes | characteristic |
| 245 | C22×C3×C4 | — | 2 | 3 | no | — |
| 246 | C2×#67 | — | 2 | 1 | no | — |
| 247 | C22×Dic3 | — | 2 | 1 | no | — |
| 248 | C22×Dic3 | — | 2 | 3 | no | — |
| 249 | D3×Q8 | — | 2 | 4 | no | — |
| 250 | D3×Q8 | — | 2 | 2 | no | — |
| 251 | D3×Q8 | — | 8 | 6 | no | — |
| 252 | D3×Q8 | C2×Q8 | 1 | 4 | yes | complemented |
| 253 | #237 | — | 2 | 2 | no | — |
| 254 | #237 | C2×Q8 | 1 | 4 | yes | — |
| 255 | C2×C4×D3 | — | 2 | 1 | no | — |
| 256 | C2×C4×D3 | — | 2 | 3 | no | — |
| 257 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 258 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 259 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 260 | C2×Dic6 | — | 2 | 1 | no | — |
| 261 | C2×Dic6 | — | 2 | 3 | no | — |
| 262 | C2×Dic6 | — | 2 | 3 | no | — |
| 263 | C2×Dic6 | — | 2 | 6 | no | — |
| 264 | C2×Dic6 | C2×D4 | 1 | 3 | yes | — |
| 265 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 266 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 267 | C3×SD16 | C2×Q8 | 1 | 4 | yes | complemented |
| 268 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 269 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 270 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 271 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 272 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 273 | C3×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 274 | C3×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 275 | C3×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 276 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 277 | C3×C42 | — | 2 | 3 | no | — |
| 278 | C3×C42 | C24 | 1 | 3 | yes | — |
| 279 | #217 | — | 2 | 3 | no | — |
| 280 | #216 | C2×Q8 | 1 | 4 | yes | complemented |
| 281 | #214 | C2×Q8 | 1 | 4 | yes | complemented |
| 282 | (C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 283 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 284 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 285 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 286 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 287 | C4⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 288 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 289 | C4⋊Dic3 | C24 | 1 | 3 | yes | — |
| 290 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 291 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 292 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 293 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 294 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 295 | Dic3⋊C4 | — | 2 | 3 | no | — |
| 296 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 297 | Dic3⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 298 | C4×Dic3 | — | 2 | 3 | no | — |
| 299 | C4×Dic3 | — | 2 | 3 | no | — |
| 300 | C4×Dic3 | — | 2 | 3 | no | — |
| 301 | C4×Dic3 | — | 2 | 3 | no | — |
| 302 | C4×Dic3 | — | 2 | 3 | no | — |
| 303 | C4×Dic3 | — | 2 | 3 | no | — |
| 304 | C4×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 305 | C4×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 306 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 307 | C2×C3⋊C8 | C24 | 1 | 3 | yes | — |
| 308 | C2×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 309 | Dic12 | C2×Q8 | 1 | 4 | yes | complemented |
| 310 | ΓL(1,𝔽25) | — | 2 | 6 | no | — |
| 311 | ΓL(1,𝔽25) | C2×Q8 | 1 | 4 | yes | complemented |
| 312 | C2×#41 | — | 3 | 1 | no | — |
| 313 | C22×Q8 | — | 2 | 1 | no | — |
| 314 | C22×Q8 | — | 3 | 1 | no | — |
| 315 | C22×Q8 | — | 3 | 1 | no | — |
| 316 | C22×Q8 | — | 6 | 3 | no | — |
| 317 | #137 | — | 3 | 8 | no | — |
| 318 | C2×Q16 | — | 3 | 1 | no | — |
| 319 | C2×Q16 | — | 3 | 1 | no | — |
| 320 | C2×SD16 | — | 3 | 1 | no | — |
| 321 | C2×SD16 | C22×D3 | 1 | 1 | yes | characteristic |
| 322 | C2×M16 | — | 3 | 1 | no | — |
| 323 | C2×M16 | — | 3 | 3 | no | — |
| 324 | C4⋊Q8 | — | 2 | 3 | no | — |
| 325 | C4⋊Q8 | — | 3 | 6 | no | — |
| 326 | C4⋊Q8 | — | 3 | 3 | no | — |
| 327 | C4⋊Q8 | — | 3 | 3 | no | — |
| 328 | C4⋊Q8 | — | 6 | 3 | no | — |
| 329 | C4⋊Q8 | — | 6 | 3 | no | — |
| 330 | C4⋊Q8 | — | 6 | 3 | no | — |
| 331 | C4⋊Q8 | — | 6 | 6 | no | — |
| 332 | C4⋊Q8 | — | 6 | 3 | no | — |
| 333 | C4⋊Q8 | — | 6 | 6 | no | — |
| 334 | C4⋊Q8 | — | 6 | 3 | no | — |
| 335 | C4⋊Q8 | — | 6 | 3 | no | — |
| 336 | C4⋊Q8 | — | 6 | 3 | no | — |
| 337 | C4⋊Q8 | C22×D3 | 1 | 3 | yes | — |
| 338 | C4⋊Q8 | C22×D3 | 1 | 3 | yes | — |
| 339 | #125 | — | 3 | 6 | no | — |
| 340 | #125 | — | 6 | 6 | no | — |
| 341 | C22⋊Q8 | — | 2 | 3 | no | — |
| 342 | C22⋊Q8 | — | 6 | 6 | no | — |
| 343 | C22⋊Q8 | — | 6 | 3 | no | — |
| 344 | C22⋊Q8 | — | 6 | 3 | no | — |
| 345 | C22⋊Q8 | — | 6 | 3 | no | — |
| 346 | C4×Q8 | — | 2 | 1 | no | — |
| 347 | C4×Q8 | — | 3 | 1 | no | — |
| 348 | C4×Q8 | — | 3 | 3 | no | — |
| 349 | C4×Q8 | — | 3 | 3 | no | — |
| 350 | C4×Q8 | — | 3 | 3 | no | — |
| 351 | C4×Q8 | — | 3 | 3 | no | — |
| 352 | C4×Q8 | — | 3 | 3 | no | — |
| 353 | C4×Q8 | — | 3 | 3 | no | — |
| 354 | C4×Q8 | — | 3 | 3 | no | — |
| 355 | C4×Q8 | — | 6 | 3 | no | — |
| 356 | C4×Q8 | — | 6 | 3 | no | — |
| 357 | C4×Q8 | — | 6 | 3 | no | — |
| 358 | C4×Q8 | — | 6 | 3 | no | — |
| 359 | C4×Q8 | — | 6 | 3 | no | — |
| 360 | C4×Q8 | — | 6 | 3 | no | — |
| 361 | C4×Q8 | — | 6 | 3 | no | — |
| 362 | C4×Q8 | — | 6 | 1 | no | — |
| 363 | C4×Q8 | — | 6 | 1 | no | — |
| 364 | C4×Q8 | C22×D3 | 1 | 3 | yes | — |
| 365 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 366 | C4×D4 | — | 3 | 3 | no | — |
| 367 | C4×D4 | — | 6 | 3 | no | — |
| 368 | C4×D4 | — | 6 | 3 | no | — |
| 369 | C4×D4 | C22×D3 | 1 | 3 | yes | — |
| 370 | #117 | — | 3 | 3 | no | — |
| 371 | #117 | — | 6 | 3 | no | — |
| 372 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 373 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 374 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 375 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 376 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 377 | C2×C42 | — | 3 | 3 | no | — |
| 378 | C2×C42 | — | 6 | 3 | no | — |
| 379 | C2×C42 | — | 6 | 3 | no | — |
| 380 | #107 | — | 3 | 3 | no | — |
| 381 | #107 | — | 3 | 6 | no | — |
| 382 | #107 | — | 3 | 3 | no | — |
| 383 | #107 | — | 3 | 6 | no | — |
| 384 | #106 | — | 3 | 3 | no | — |
| 385 | #106 | — | 3 | 6 | no | — |
| 386 | #106 | C22×D3 | 1 | 3 | yes | — |
| 387 | #106 | C22×D3 | 1 | 6 | yes | — |
| 388 | C4⋊C8 | — | 3 | 6 | no | — |
| 389 | C4⋊C8 | — | 3 | 3 | no | — |
| 390 | C4⋊C8 | C22×D3 | 1 | 3 | yes | — |
| 391 | #103 | — | 3 | 3 | no | — |
| 392 | #103 | — | 3 | 3 | no | — |
| 393 | #103 | — | 3 | 3 | no | — |
| 394 | #103 | — | 3 | 3 | no | — |
| 395 | #103 | — | 3 | 3 | no | — |
| 396 | #103 | C22×D3 | 1 | 3 | yes | — |
| 397 | #102 | — | 3 | 3 | no | — |
| 398 | #102 | C22×D3 | 1 | 3 | yes | — |
| 399 | #97 | — | 3 | 3 | no | — |
| 400 | #97 | — | 3 | 3 | no | — |
| 401 | C4×C8 | — | 3 | 3 | no | — |
| 402 | C4×C8 | C22×D3 | 1 | 3 | yes | — |
| 403 | C23×C3 | — | 2 | 1 | no | — |
| 404 | C22×D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 405 | C3×Q8 | — | 2 | 1 | no | — |
| 406 | C3×Q8 | — | 4 | 6 | no | — |
| 407 | C3×Q8 | — | 8 | 3 | no | — |
| 408 | C3×Q8 | #137 | 1 | 4 | yes | complemented |
| 409 | C3×Q8 | C22×Q8 | 1 | 2 | yes | — |
| 410 | C3×D4 | — | 2 | 1 | no | — |
| 411 | C3×D4 | C22×Q8 | 1 | 2 | yes | — |
| 412 | C2×C3×C4 | — | 2 | 1 | no | — |
| 413 | C2×C3×C4 | — | 2 | 3 | no | — |
| 414 | C2×C3×C4 | — | 2 | 3 | no | — |
| 415 | C2×C3×C4 | — | 4 | 6 | no | — |
| 416 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 417 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 418 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 419 | #67 | — | 2 | 4 | no | — |
| 420 | C2×Dic3 | — | 2 | 1 | no | — |
| 421 | C2×Dic3 | — | 2 | 1 | no | — |
| 422 | C2×Dic3 | — | 2 | 4 | no | — |
| 423 | C2×Dic3 | — | 2 | 3 | no | — |
| 424 | C2×Dic3 | — | 2 | 3 | no | — |
| 425 | C2×Dic3 | — | 8 | 3 | no | — |
| 426 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 427 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 428 | C2×Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 429 | C4×D3 | — | 2 | 4 | no | — |
| 430 | C4×D3 | — | 2 | 6 | no | — |
| 431 | C4×D3 | — | 4 | 3 | no | — |
| 432 | C4×D3 | — | 4 | 6 | no | — |
| 433 | C4×D3 | C22×Q8 | 1 | 2 | yes | — |
| 434 | C4×D3 | 2−1+4 | 1 | 2 | yes | — |
| 435 | Dic6 | — | 2 | 6 | no | — |
| 436 | Dic6 | — | 2 | 1 | no | — |
| 437 | Dic6 | — | 2 | 1 | no | — |
| 438 | Dic6 | — | 2 | 4 | no | — |
| 439 | Dic6 | — | 8 | 6 | no | — |
| 440 | Dic6 | — | 8 | 3 | no | — |
| 441 | Dic6 | — | 8 | 3 | no | — |
| 442 | Dic6 | C22×Q8 | 1 | 2 | yes | — |
| 443 | Dic6 | C22×Q8 | 1 | 2 | yes | — |
| 444 | C3×C8 | — | 2 | 3 | no | — |
| 445 | C3×C8 | C22×Q8 | 1 | 2 | yes | — |
| 446 | C3⋊C8 | — | 2 | 3 | no | — |
| 447 | C3⋊C8 | C22×Q8 | 1 | 2 | yes | — |
| 448 | #41 | — | 3 | 4 | no | — |
| 449 | #41 | — | 6 | 2 | no | — |
| 450 | C2×Q8 | — | 2 | 3 | no | — |
| 451 | C2×Q8 | — | 2 | 3 | no | — |
| 452 | C2×Q8 | — | 3 | 3 | no | — |
| 453 | C2×Q8 | — | 3 | 4 | no | — |
| 454 | C2×Q8 | — | 3 | 1 | no | — |
| 455 | C2×Q8 | — | 3 | 1 | no | — |
| 456 | C2×Q8 | — | 4 | 4 | no | — |
| 457 | C2×Q8 | — | 6 | 1 | no | — |
| 458 | C2×Q8 | — | 6 | 6 | no | — |
| 459 | C2×Q8 | — | 6 | 2 | no | — |
| 460 | C2×Q8 | — | 6 | 4 | no | — |
| 461 | C2×Q8 | — | 6 | 3 | no | — |
| 462 | C2×Q8 | — | 6 | 3 | no | — |
| 463 | C2×Q8 | — | 24 | 6 | no | — |
| 464 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 465 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 466 | C2×D4 | — | 6 | 1 | no | — |
| 467 | C2×D4 | C23×D3 | 1 | 1 | yes | characteristic |
| 468 | C22×C4 | — | 2 | 3 | no | — |
| 469 | C22×C4 | — | 3 | 1 | no | — |
| 470 | C22×C4 | — | 3 | 3 | no | — |
| 471 | C22×C4 | — | 3 | 3 | no | — |
| 472 | C22×C4 | — | 6 | 1 | no | — |
| 473 | C22×C4 | — | 6 | 3 | no | — |
| 474 | C22×C4 | — | 6 | 1 | no | — |
| 475 | C22×C4 | — | 6 | 3 | no | — |
| 476 | Q16 | — | 3 | 4 | no | — |
| 477 | Q16 | — | 3 | 4 | no | — |
| 478 | SD16 | — | 3 | 4 | no | — |
| 479 | SD16 | D3×Q8 | 1 | 4 | yes | complemented |
| 480 | M16 | — | 3 | 4 | no | — |
| 481 | M16 | — | 6 | 6 | no | — |
| 482 | C2×C8 | — | 3 | 1 | no | — |
| 483 | C2×C8 | — | 3 | 3 | no | — |
| 484 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 485 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 486 | C4⋊C4 | — | 2 | 3 | no | — |
| 487 | C4⋊C4 | — | 2 | 3 | no | — |
| 488 | C4⋊C4 | — | 2 | 3 | no | — |
| 489 | C4⋊C4 | — | 3 | 3 | no | — |
| 490 | C4⋊C4 | — | 3 | 6 | no | — |
| 491 | C4⋊C4 | — | 3 | 3 | no | — |
| 492 | C4⋊C4 | — | 3 | 3 | no | — |
| 493 | C4⋊C4 | — | 6 | 3 | no | — |
| 494 | C4⋊C4 | — | 6 | 3 | no | — |
| 495 | C4⋊C4 | — | 6 | 3 | no | — |
| 496 | C4⋊C4 | — | 6 | 6 | no | — |
| 497 | C4⋊C4 | — | 6 | 6 | no | — |
| 498 | C4⋊C4 | — | 6 | 3 | no | — |
| 499 | C4⋊C4 | — | 6 | 6 | no | — |
| 500 | C4⋊C4 | — | 6 | 3 | no | — |
| 501 | C4⋊C4 | — | 6 | 3 | no | — |
| 502 | C4⋊C4 | — | 6 | 3 | no | — |
| 503 | C4⋊C4 | — | 6 | 3 | no | — |
| 504 | C4⋊C4 | D3×D4 | 1 | 3 | yes | — |
| 505 | C4⋊C4 | C23×D3 | 1 | 3 | yes | — |
| 506 | C4⋊C4 | C23×D3 | 1 | 3 | yes | — |
| 507 | C22⋊C4 | — | 2 | 3 | no | — |
| 508 | C22⋊C4 | — | 6 | 3 | no | — |
| 509 | C22⋊C4 | — | 6 | 3 | no | — |
| 510 | C42 | — | 2 | 3 | no | — |
| 511 | C42 | — | 3 | 3 | no | — |
| 512 | C42 | — | 3 | 3 | no | — |
| 513 | C42 | — | 3 | 3 | no | — |
| 514 | C42 | — | 6 | 3 | no | — |
| 515 | C42 | — | 6 | 3 | no | — |
| 516 | C42 | — | 6 | 3 | no | — |
| 517 | C42 | — | 6 | 3 | no | — |
| 518 | C42 | — | 6 | 3 | no | — |
| 519 | C42 | — | 6 | 3 | no | — |
| 520 | C42 | C23×D3 | 1 | 3 | yes | — |
| 521 | C22×C3 | — | 2 | 2 | no | — |
| 522 | C22×C3 | — | 4 | 1 | no | — |
| 523 | C22×C3 | — | 4 | 1 | no | — |
| 524 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 525 | C2×D3 | — | 2 | 1 | no | — |
| 526 | C2×D3 | — | 2 | 1 | no | — |
| 527 | C2×D3 | D4×Q8 | 1 | 2 | yes | — |
| 528 | C3×C4 | — | 2 | 3 | no | — |
| 529 | C3×C4 | — | 2 | 2 | no | — |
| 530 | C3×C4 | — | 4 | 3 | no | — |
| 531 | C3×C4 | — | 4 | 3 | no | — |
| 532 | C3×C4 | C2×#137 | 1 | 6 | yes | — |
| 533 | C3×C4 | C23×Q8 | 1 | 1 | yes | characteristic |
| 534 | C3×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 535 | Dic3 | — | 2 | 3 | no | — |
| 536 | Dic3 | — | 2 | 2 | no | — |
| 537 | Dic3 | — | 2 | 2 | no | — |
| 538 | Dic3 | — | 2 | 3 | no | — |
| 539 | Dic3 | — | 4 | 3 | no | — |
| 540 | Dic3 | — | 4 | 3 | no | — |
| 541 | Dic3 | D4×Q8 | 1 | 2 | yes | — |
| 542 | C23 | — | 2 | 1 | no | — |
| 543 | C23 | — | 3 | 1 | no | — |
| 544 | Q8 | — | 2 | 1 | no | — |
| 545 | Q8 | — | 3 | 2 | no | — |
| 546 | Q8 | — | 3 | 2 | no | — |
| 547 | Q8 | — | 4 | 6 | no | — |
| 548 | Q8 | — | 6 | 4 | no | — |
| 549 | Q8 | — | 6 | 1 | no | — |
| 550 | Q8 | — | 6 | 1 | no | — |
| 551 | Q8 | — | 6 | 6 | no | — |
| 552 | Q8 | — | 8 | 3 | no | — |
| 553 | Q8 | — | 24 | 3 | no | — |
| 554 | Q8 | — | 24 | 3 | no | — |
| 555 | Q8 | — | 24 | 6 | no | — |
| 556 | Q8 | #915 | 1 | 4 | yes | direct product factor |
| 557 | Q8 | C2×D3×Q8 | 1 | 2 | yes | — |
| 558 | D4 | — | 2 | 1 | no | — |
| 559 | D4 | — | 6 | 4 | no | — |
| 560 | D4 | C2×D3×Q8 | 1 | 2 | yes | — |
| 561 | C2×C4 | — | 2 | 1 | no | — |
| 562 | C2×C4 | — | 2 | 3 | no | — |
| 563 | C2×C4 | — | 2 | 3 | no | — |
| 564 | C2×C4 | — | 3 | 1 | no | — |
| 565 | C2×C4 | — | 3 | 2 | no | — |
| 566 | C2×C4 | — | 3 | 2 | no | — |
| 567 | C2×C4 | — | 3 | 3 | no | — |
| 568 | C2×C4 | — | 3 | 3 | no | — |
| 569 | C2×C4 | — | 4 | 6 | no | — |
| 570 | C2×C4 | — | 6 | 4 | no | — |
| 571 | C2×C4 | — | 6 | 4 | no | — |
| 572 | C2×C4 | — | 6 | 1 | no | — |
| 573 | C2×C4 | — | 6 | 1 | no | — |
| 574 | C2×C4 | — | 6 | 6 | no | — |
| 575 | C2×C4 | — | 6 | 3 | no | — |
| 576 | C2×C4 | — | 6 | 3 | no | — |
| 577 | C2×C4 | — | 12 | 3 | no | — |
| 578 | C2×C4 | — | 12 | 6 | no | — |
| 579 | C2×C4 | — | 24 | 3 | no | — |
| 580 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 581 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 582 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 583 | C8 | — | 2 | 3 | no | — |
| 584 | C8 | — | 3 | 2 | no | — |
| 585 | C8 | — | 6 | 3 | no | — |
| 586 | C8 | C2×D3×Q8 | 1 | 2 | yes | — |
| 587 | C2×C3 | — | 4 | 2 | no | — |
| 588 | C2×C3 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 589 | C2×C3 | C22×#137 | 1 | 1 | yes | characteristic |
| 590 | C2×C3 | #3585 | 1 | 1 | yes | characteristic |
| 591 | D3 | — | 2 | 2 | no | — |
| 592 | C22 | — | 2 | 2 | no | — |
| 593 | C22 | — | 3 | 2 | no | — |
| 594 | C22 | — | 4 | 1 | no | — |
| 595 | C22 | — | 4 | 1 | no | — |
| 596 | C22 | — | 6 | 1 | no | — |
| 597 | C22 | — | 6 | 1 | no | — |
| 598 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 599 | C4 | — | 2 | 3 | no | — |
| 600 | C4 | — | 2 | 2 | no | — |
| 601 | C4 | — | 3 | 2 | no | — |
| 602 | C4 | — | 4 | 3 | no | — |
| 603 | C4 | — | 4 | 3 | no | — |
| 604 | C4 | — | 6 | 3 | no | — |
| 605 | C4 | — | 6 | 3 | no | — |
| 606 | C4 | — | 6 | 2 | no | — |
| 607 | C4 | — | 6 | 2 | no | — |
| 608 | C4 | — | 12 | 3 | no | — |
| 609 | C4 | — | 12 | 3 | no | — |
| 610 | C4 | C2×#915 | 1 | 6 | yes | — |
| 611 | C4 | C22×D3×Q8 | 1 | 1 | yes | characteristic |
| 612 | C4 | D3×2−1+4 | 1 | 1 | yes | characteristic |
| 613 | C3 | Q8×#137 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 614 | C2 | — | 4 | 2 | no | — |
| 615 | C2 | — | 6 | 2 | no | — |
| 616 | C2 | D3×D4×Q8 | 1 | 1 | yes | characteristic |
| 617 | C2 | C22×#915 | 1 | 1 | yes | characteristic |
| 618 | C2 | #87207 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×Q82 | C2 | semidirect |
| 3. C3×Q8×SD16 | C2 | semidirect |
| 4. Q8×#216 | C2 | semidirect |
| 5. Q8×#214 | C2 | semidirect |
| 6. #81906 | C2 | semidirect |
| 7. #81893 | C2 | semidirect |
| 9. #81056 | C2 | semidirect |
| 10. #81043 | C2 | semidirect |
| 11. #81011 | C2 | semidirect |
| 12. Q8×Dic12 | C2 | semidirect |
| 13. Q8×ΓL(1,𝔽25) | C2 | semidirect |
| 15. #79634 | C2 | semidirect |
| 84. Q8×SD16 | D3 | semidirect |
| 121. #915 | Q8 | direct (N × H) |
| 252. D3×Q8 | C2×Q8 | semidirect |
| 267. C3×SD16 | C2×Q8 | semidirect |
| 280. #216 | C2×Q8 | semidirect |
| 281. #214 | C2×Q8 | semidirect |
| 309. Dic12 | C2×Q8 | semidirect |
| 311. ΓL(1,𝔽25) | C2×Q8 | semidirect |
| 408. C3×Q8 | #137 | semidirect |
| 479. SD16 | D3×Q8 | semidirect |
| 556. Q8 | #915 | direct (N × H) |
| 613. C3 | Q8×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q82 | 2 |
| Q8×#237 | 2 |
| C3×Q8×SD16 | 2 |
| Q8×#216 | 2 |
| Q8×#214 | 2 |
| #81906 | 2 |
| #81893 | 2 |
| #81061 | 2 |
| #81056 | 2 |
| #81043 | 2 |
| #81011 | 2 |
| Q8×Dic12 | 2 |
| Q8×ΓL(1,𝔽25) | 2 |
| C4×#915 | 2 |
| #79634 | 2 |
| Q8×#137 | 3 |